version 1.3, 2002/09/27 08:40:48 |
version 1.4, 2002/09/30 06:13:07 |
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/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.2 2002/09/26 09:07:42 noro Exp $ */ |
/* $OpenXM: OpenXM_contrib2/asir2000/engine/Fgfs.c,v 1.3 2002/09/27 08:40:48 noro Exp $ */ |
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#include "ca.h" |
#include "ca.h" |
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Line 6 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp); |
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Line 6 void cont_pp_mv_sf(VL vl,VL rvl,P p,P *c,P *pp); |
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void gcdsf_main(VL vl,P *pa,int m,P *r); |
void gcdsf_main(VL vl,P *pa,int m,P *r); |
void ugcdsf(P *pa,int m,P *r); |
void ugcdsf(P *pa,int m,P *r); |
void head_monomial(V v,P p,P *coef,P *term); |
void head_monomial(V v,P p,P *coef,P *term); |
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void sqfrsfmain(VL vl,P f,DCP *dcp); |
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void pthrootsf(P f,Q m,P *r); |
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void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp); |
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void gcdsf(VL vl,P *pa,int k,P *r); |
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void lex_lc(P f,P *c) |
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{ |
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if ( !f || NUM(f) ) |
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*c = f; |
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else |
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lex_lc(COEF(DC(f)),c); |
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} |
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DCP append_dc(DCP dc,DCP dct) |
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{ |
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DCP dcs; |
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if ( !dc ) |
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return dct; |
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else { |
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for ( dcs = dc; NEXT(dcs); dcs = NEXT(dcs) ); |
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NEXT (dcs) = dct; |
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return dc; |
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} |
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} |
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void sqfrsf(VL vl, P f, DCP *dcp) |
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{ |
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DCP dc,dct; |
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Obj obj; |
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P t,s,c; |
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VL tvl,nvl; |
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simp_ff((Obj)f,&obj); f = (P)obj; |
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lex_lc(f,&c); divsp(vl,f,c,&t); f = t; |
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monomialfctr(vl,f,&t,&dc); f = t; |
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clctv(vl,f,&tvl); vl = tvl; |
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if ( !vl ) |
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; |
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else if ( !NEXT(vl) ) { |
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sfusqfr(f,&dct); |
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dc = append_dc(dc,NEXT(dct)); |
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} else { |
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t = f; |
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for ( tvl = vl; tvl; tvl = NEXT(tvl) ) { |
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reordvar(vl,tvl->v,&nvl); |
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cont_pp_mv_sf(vl,NEXT(nvl),t,&c,&s); t = s; |
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sqfrsf(vl,c,&dct); |
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dc = append_dc(dc,NEXT(dct)); |
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} |
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sqfrsfmain(vl,t,&dct); |
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dc = append_dc(dc,dct); |
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} |
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NEWDC(dct); DEG(dct) = ONE; COEF(dct) = (P)c; NEXT(dct) = dc; |
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*dcp = dct; |
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} |
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void sqfrsfmain(VL vl,P f,DCP *dcp) |
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{ |
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VL tvl; |
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DCP dc,dct,dcs; |
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P t,s; |
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Q m,m1; |
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V v; |
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clctv(vl,f,&tvl); vl = tvl; |
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dc = 0; |
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t = f; |
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for ( tvl = vl; tvl; tvl = NEXT(tvl) ) { |
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v = tvl->v; |
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partial_sqfrsf(vl,v,t,&s,&dct); t = s; |
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dc = append_dc(dc,dct); |
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} |
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if ( !NUM(t) ) { |
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STOQ(characteristic_sf(),m); |
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pthrootsf(t,m,&s); |
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sqfrsfmain(vl,s,&dct); |
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for ( dcs = dct; dcs; dcs = NEXT(dcs) ) { |
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mulq(DEG(dcs),m,&m1); DEG(dcs) = m1; |
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} |
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dc = append_dc(dc,dct); |
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} |
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*dcp = dc; |
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} |
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void pthrootsf(P f,Q m,P *r) |
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{ |
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DCP dc,dc0,dct; |
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N qn,rn; |
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if ( NUM(f) ) |
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pthrootgfs(f,r); |
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else { |
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dc = DC(f); |
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dc0 = 0; |
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for ( dc0 = 0; dc; dc = NEXT(dc) ) { |
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NEXTDC(dc0,dct); |
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pthrootsf(COEF(dc),m,&COEF(dct)); |
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if ( DEG(dc) ) { |
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divn(NM(DEG(dc)),NM(m),&qn,&rn); |
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if ( rn ) |
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error("pthrootsf : cannot happen"); |
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NTOQ(qn,1,DEG(dct)); |
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} else |
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DEG(dct) = 0; |
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} |
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NEXT(dct) = 0; |
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MKP(VR(f),dc0,*r); |
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} |
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} |
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void partial_sqfrsf(VL vl,V v,P f,P *r,DCP *dcp) |
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{ |
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P ps[2]; |
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DCP dc0,dc; |
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int m; |
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P t,flat,flat1,g,df,q; |
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diffp(vl,f,v,&df); |
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if ( !df ) { |
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*dcp = 0; |
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*r = f; |
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return; |
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} |
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ps[0] = f; ps[1] = df; |
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gcdsf(vl,ps,2,&g); |
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divsp(vl,f,g,&flat); |
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m = 0; |
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t = f; |
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dc0 = 0; |
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while ( !NUM(flat) ) { |
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while ( divtp(vl,t,flat,&q) ) { |
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t = q; m++; |
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} |
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ps[0] = t; ps[1] = flat; |
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gcdsf(vl,ps,2,&flat1); |
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divsp(vl,flat,flat1,&g); |
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flat = flat1; |
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NEXTDC(dc0,dc); |
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COEF(dc) = g; |
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STOQ(m,DEG(dc)); |
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} |
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NEXT(dc) = 0; |
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*dcp = dc0; |
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*r = t; |
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} |
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void gcdsf(VL vl,P *pa,int k,P *r) |
void gcdsf(VL vl,P *pa,int k,P *r) |
{ |
{ |
P *ps,*pl,*pm; |
P *ps,*pl,*pm; |
Line 113 void ugcdsf(P *pa,int m,P *r) |
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Line 259 void ugcdsf(P *pa,int m,P *r) |
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sfumtop(v,w1,r); |
sfumtop(v,w1,r); |
} |
} |
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/* deg(HT(p),v), where p is considered as distributed poly over F[v] */ |
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int gethdeg(VL vl,V v,P p) |
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{ |
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DCP dc; |
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Q dmax; |
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P cmax; |
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if ( !p ) |
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return -1; |
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else if ( NUM(p) ) |
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return 0; |
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else if ( VR(p) != v ) |
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/* HT(p) = HT(lc(p))*x^D */ |
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return gethdeg(vl,v,COEF(DC(p))); |
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else { |
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/* VR(p) = v */ |
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dc = DC(p); dmax = DEG(dc); cmax = COEF(dc); |
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for ( dc = NEXT(dc); dc; dc = NEXT(dc) ) |
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if ( compp(vl,COEF(dc),cmax) > 0 ) { |
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dmax = DEG(dc); cmax = COEF(dc); |
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} |
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return QTOS(dmax); |
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} |
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} |
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/* all the pa[i]'s have the same variables (=vl) */ |
/* all the pa[i]'s have the same variables (=vl) */ |
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void gcdsf_main(VL vl,P *pa,int m,P *r) |
void gcdsf_main(VL vl,P *pa,int m,P *r) |
Line 131 void gcdsf_main(VL vl,P *pa,int m,P *r) |
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Line 301 void gcdsf_main(VL vl,P *pa,int m,P *r) |
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ugcdsf(pa,m,r); |
ugcdsf(pa,m,r); |
return; |
return; |
} |
} |
/* find v s.t. min(deg(pa[i],v)) is minimal */ |
/* find v s.t. min(deg(pa[i],v)+gethdeg(pa[i],v)) is minimal */ |
tvl = vl; |
tvl = vl; |
do { |
do { |
v = tvl->v; |
v = tvl->v; |
i = 0; |
i = 0; |
do { |
do { |
d = getdeg(v,pa[i]); |
d = getdeg(v,pa[i])+gethdeg(vl,v,pa[i]); |
if ( i == 0 || (d < d0) ) { |
if ( i == 0 || (d < d0) ) { |
d0 = d; i0 = i; v0 = v; |
d0 = d; i0 = i; v0 = v; |
} |
} |